Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

Mohamed A. Abdelkawy; Ahmed Z.M. Amin; António M. Lopes; Ishak Hashim; Mohammed M. Babatin

doi:10.3390/fractalfract6010019

Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

Mohamed A. Abdelkawy
, Ahmed Z.M. Amin
, António M. Lopes
, Ishak Hashim
, Mohammed M. Babatin

Al-Imam Muhammad Ibn Saud Islamic University
Faculty of Sciences
Universiti Kebangsaan Malaysia
University of Porto

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.

Original language	English
Article number	19
Journal	Fractal and Fractional
Volume	6
Issue number	1
DOIs	https://doi.org/10.3390/fractalfract6010019
State	Published - Jan 2022
Externally published	Yes

Keywords

Fractional-order shifted Jacobi polynomial
Riemann–Liouville fractional derivative
Riemann–Liouville fractional integral
Variable-order fractional integro-differential equation

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10.3390/fractalfract6010019

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title = "Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel",

abstract = "We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.",

keywords = "Fractional-order shifted Jacobi polynomial, Riemann–Liouville fractional derivative, Riemann–Liouville fractional integral, Variable-order fractional integro-differential equation",

author = "Abdelkawy, \{Mohamed A.\} and Amin, \{Ahmed Z.M.\} and Lopes, \{Ant{\'o}nio M.\} and Ishak Hashim and Babatin, \{Mohammed M.\}",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2022",

month = jan,

doi = "10.3390/fractalfract6010019",

language = "English",

volume = "6",

journal = "Fractal and Fractional",

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T1 - Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

AU - Abdelkawy, Mohamed A.

AU - Amin, Ahmed Z.M.

AU - Lopes, António M.

AU - Hashim, Ishak

AU - Babatin, Mohammed M.

PY - 2022/1

Y1 - 2022/1

N2 - We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.

AB - We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.

KW - Fractional-order shifted Jacobi polynomial

KW - Riemann–Liouville fractional derivative

KW - Riemann–Liouville fractional integral

KW - Variable-order fractional integro-differential equation

UR - https://www.scopus.com/pages/publications/85123802506

U2 - 10.3390/fractalfract6010019

DO - 10.3390/fractalfract6010019

M3 - Article

AN - SCOPUS:85123802506

SN - 2504-3110

VL - 6

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 1

M1 - 19

ER -

Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

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Keywords

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